Technical Papers
Jan 31, 2022

Analysis of Tensegrity Rotationally Repetitive Space Structures Using the Substructuring Method

Publication: Practice Periodical on Structural Design and Construction
Volume 27, Issue 2

Abstract

In this paper, a substructuring method is presented for calculating the displacement of cable domes. This method obtained matrices as a canonical form in cyclic structures using graph theory. This method helps to avoid the generation of the entire matrices. Then, a solution for the eigenproblem is presented and nonlinear equations are solved by the Newton–Raphson method. In this paper, the cable domes are prestressed rotationally repetitive structures that are cyclically symmetric, having cable part and compression strut part. For clarifying the benefits of the proposed method, both the usual method and the substructuring method are performed for some examples. Results show that the time and memory are considerably (more than 80%) saved in the substructuring approach.

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Data Availability Statement

All data, models, and code generated or used during the study appear in the published article.

References

Abedi, K., and G. Parke. 1996. “Progressive collapse of single-layer braced domes.” Int. J. Space Struct. 11 (3): 291–306. https://doi.org/10.1177/026635119601100302.
Aghayere, A. O. 1983. “Structural systems with polar symmetry: Solution by quasicirculant matrices.” Doctoral dissertation, Dept. of Civil Engineering, Massachusetts Institute of Technology.
Chen, Y., and J. Feng. 2012. “Generalized eigenvalue analysis of symmetric prestressed structures using group theory.” J. Comput. Civ. Eng. 26 (4): 488–497. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000151.
Chen, Y., J. Feng, L. Zhuang, and S. Xia. 2012. “Elastic stability of symmetric dome structures using group theory.” In Proc., Earth and Space 2012: Engineering, Science, Construction, and Operations in Challenging Environments, 655–663. Reston, VA: ASCE. https://doi.org/10.1061/9780784412190.071.
Geiger, D. H., A. Stefaniuk, and D. Chen. 1986. “The design and construction of two cable domes for the Korean Olympics.” In Proc., IASS Symp. on Shells, Membranes and Space Frames. Amsterdam, Netherlands: Elsevier Science Publishers BV.
Gurfinkel, G., and S. Krishnan. 2017. “Analysis and design of cable-stayed steel columns using the stiffness probe method.” Eng. J. Am. Inst. Steel Constr. 54 (3): 195–210.
Han, Q., and X. Liu. 2002. “Behavior of a single layer spherical dome with openings and large depth-to-span ratio.” Adv. Struct. Eng. 5 (3): 137–142. https://doi.org/10.1260/136943302760228086.
Hasan, M. A., and J. A. Hasan. 2002. “Block eigenvalue decomposition using nth roots of the identity matrix.” In Proc., 41st IEEE Conf. on Decision and Control, 2002. New York: IEEE.
Kangwai, R., S. Guest, and S. Pellegrino. 1999. “An introduction to the analysis of symmetric structures.” Comput. Struct. 71 (6): 671–688. https://doi.org/10.1016/S0045-7949(98)00234-X.
Kaveh, A. 2004. Structural mechanics: Graph and matrix methods. Somerset, UK: Research Studies Press.
Kaveh, A. 2013. Optimal structural analysis using the concept of symmetry and regularity. Berlin: Springer.
Kaveh, A., and F. Nemati. 2010. “Eigensolution of rotationally repetitive space structures using a canonical form.” Int. J. Numer. Methods Biomed. Eng. 26 (12): 1781–1796. https://doi.org/10.1002/cnm.1265.
Kaveh, A., and H. Rahami. 2006. “Block diagonalization of adjacency and Laplacian matrices for graph product; applications in structural mechanics.” Int. J. Numer. Methods Eng. 68 (1): 33–63. https://doi.org/10.1002/nme.1696.
Kaveh, A., and B. Salimbahrami. 2004. “Eigensolution of symmetric frames using graph factorization.” Commun. Numer. Methods Eng. 20 (12): 889–910. https://doi.org/10.1002/cnm.711.
Kaveh, A., and M. Sayarinejad. 2005. “Eigenvalues of factorable matrices with form IV symmetry.” Commun. Numer. Methods Eng. 21 (6): 269–287. https://doi.org/10.1002/cnm.744.
Kebiche, K., M. Kazi-Aoual, and R. Motro. 1999. “Geometrical non-linear analysis of tensegrity systems.” Eng. Struct. 21 (9): 864–876. https://doi.org/10.1016/S0141-0296(98)00014-5.
Krishnan, S. 2015. Prestressed cable domes: Structural behavior and design. Champaign, IL: Univ. of Illinois at Urbana-Champaign.
Levy, M. 1989. “Hypar-tensegrity dome.” In Proc., Int. Symp. on Sports Architecture, 157–162. London: Thomas Telford.
Motro, R. 1992. “Tensegrity systems: The state of the art.” Int. J. Space Struct. 7 (2): 75–83. https://doi.org/10.1177/026635119200700201.
Motro, R. 2003. Tensegrity: Structural systems for the future. Amsterdam, Netherlands: Elsevier.
Pugh, A. 1976. An introduction to tensegrity. Berkeley, CA: University of California Press.
Rebielak, J. 2000. “Structural system of cable dome shaped by means of simple form of spatial hoops.” In Lightweight structures in civil engineering, edited by J. B. Obrebski Wydawnictwo Naukowe, 114–115. Warsaw, Poland: Micro-Publisher.
Thomas, D. L. 1979. “Dynamics of rotationally periodic structures.” Int. J. Numer. Methods Eng. 14 (1): 81–102. https://doi.org/10.1002/nme.1620140107.
Williams, F. 1986a. “An algorithm for exact eigenvalue calculations for rotationally periodic structures.” Int. J. Numer. Methods Eng. 23 (4): 609–622. https://doi.org/10.1002/nme.1620230407.
Williams, F. 1986b. “Exact eigenvalue calculations for structures with rotationally periodic substructures.” Int. J. Numer. Methods Eng. 23 (4): 695–706. https://doi.org/10.1002/nme.1620230411.
Yuan, X., and S. Dong. 2003. “Integral feasible prestress of cable domes.” Comput. Struct. 81 (21): 2111–2119. https://doi.org/10.1016/S0045-7949(03)00254-2.

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Go to Practice Periodical on Structural Design and Construction
Practice Periodical on Structural Design and Construction
Volume 27Issue 2May 2022

History

Received: Jul 14, 2021
Accepted: Dec 2, 2021
Published online: Jan 31, 2022
Published in print: May 1, 2022
Discussion open until: Jun 30, 2022

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Authors

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Ph.D. Candidate, School of Civil Engineering, Kharazmi Univ., Tehran 15719-14911, Iran (corresponding author). ORCID: https://orcid.org/0000-0002-6057-8045. Email: [email protected]
Jafar Keyvani [email protected]
Associate Professor, School of Civil Engineering, Kharazmi Univ., Tehran 15719-14911, Iran. Email: [email protected]
Professor, School of Civil Engineering, Iran Univ. of Science and Technology, Tehran 13114-16846, Iran. Email: [email protected]

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